Mother Thumping Impossible (also known as MTI) is a map created by blue_tetris. It was included in N 1.4 as level 88-4 and is widely considered the most difficult (and infamous) level of the game. It is often mistakenly called Mother Thwumping Impossible, due to the large number of thwumps.

Walkthrough

Method 1

Each tunnel is discussed (in order) in a paragraph. You should only use this if you are a complete and utter n00b.

As soon as you start, jump and hover right to collect the three pieces of gold and land on the slope past the two mines on the bottom. Jump again past the next two mines, and then jump to hit the trapdoor. Wait for the zap drone to pass by overhead to the left, and then climb into the next area where the trapdoor was sprung. Run across to the right, and jump on that slight slope. As you approach the thwump it will move downwards, giving you room to squeeze above it and enter the first vertical tunnel.

In this tunnel, on the left wall there are three protruding ledges. The goal is to land on the third one from the top, which will slow your momentum and let you slide down to the bottom right slope. If you're impatient you can immediately fall down to that slope from the previous tunnel (the extra speed might cause you to crash into a mine, however). Otherwise, stop on the first ledge, then tip over to the third ledge, then fall onto the bottom right slope and land on that thwump. Immediately hold left!

In the third tunnel, you will perform a trick in which you can ride a thwump. If you hold left, you will be running on top of the thwump (actually, you will go slightly faster than the thwump, though this shouldn't be a problem). You can choose to jump to get the arc of gold in the first cavern. In the second cavern, immediately jump upon entrance, leaping over the rightwards moving thwump, and landing on that ledge on the bottom. Tilt over to the side, and then leap off of the slope, collecting gold on the way. From there jump to the end of this tunnel.

Now you will have to climb upwards. Jump onto that little downwards slope under the bottom left ledge, and from that position carefully jump onto the little ledge above. (Its not as difficult as it looks, despite the mines). From here, you can choose to get the trapdoor or not. Getting the trapdoor greatly increases your chance of dying here but it helps slightly later on; I personally find it easier to avoid getting the trapdoor. To get the trapdoor switch, walljump off the bottom right ledge of that shaft. Otherwise, land on that ledge, then jump up the next two ledges and activate the thwump there.

There's many ways to do this next tunnel, and patience helps. At this point, I recommend pausing the game (its probably getting a bit nerve-racking by now), and uponing up Eeyore's level data program and opening 88-4 on Ned. [Enter] yourself onto this tunnel and practice it a number of times, because its frustrating to have to do the entire beginning and then dying close to the very end. Actually, what is so frustrating about this level is that it gets harder towards the end, so don't get angered if you're having difficulties with the last parts. Many players take up hours to beat this level for the first time.

Going back to this tunnel, stay on that little slope you start at and just wait there for the thwump to come by.

Congratulations on beating (at least what is considered to be) the hardest level of the game, and unlocking episode 89!

Method 2 (Aries Easy Way)

The first part (the top) is pretty simple; just don't get killed on the mines. I recommend getting the switch, but it's not actually necessary; you can run through that top part (just hold right all the way and you'll get it) and bounce off the ledge (right by where the platform would appear) and if you have your momentum going, you'll bounce right over the mines. Oh, and watch out for the drone. Easy enough, I shouldn't have to explain anything about it if you've made it this far in the game.
I'll do the rest of this thwump by thwump, or corridor by corridor (where a corridor is like one straight section that ends when the level turns)
The very first thwump is easy. Just jump straight at it and it will go down, and you will go over. I try to aim to land on the small flat ledge a little to the right of the first thwump.
Standing on that ledge triggers a thwump to come upwards towards you. Don't worry about it, there's enough room on the left side for you to fall safely while it's coming at you. So go ahead and tiptoe off the right side of the ledge and fall straight down. If you fall straight off the ledge and don't move either direction, the thwump will pass you, and you will land on a slanted ledge which will send you to the right side of the corridor onto another slanted ledge that will send you right on top of another thwump (it faces left). So for that falling part, just fall straight off that little ledge(you may have to realign yourself by tapping left once or twice) and don't press anything 'til you hit that slant that's about 45 degrees in the lower right corner that shoots you on top of the thwump(if all went right). At that point (and maybe a little before you hit the ledge), start moving left. *Alternatively*, if you're not planning to run on top of the thwump in the bottom left, you can take this part a little slower, dropping from ledge to ledge and land in the bottom right where it's safe, so you can get ready for your slow trek across the bottom(I don't like that way).
Start moving left because I found the easiest way to do this part is to just keep running on top of the thwump (really not that hard after the first or second try and it flows really well). Then jump before the thwump coming at you kills you (you should be jumping right after the first of two arches of gold). There should be a raised part in the ceiling right there for you to clear the oncoming thwump, and a flat, raised ledge (with no mines on it) for you to land on. From that ledge, you have to either teeter over the edge(so the ninja isn't standing straight up) or actually be on the slant to jump safely, because there's an overhanging slanted ceiling to block your jump(and send you into the mines) if you jump too high. You should land on a slant that faces towards you, so jump once you land on it or run left off of it, or you'll slide into a mine. So land on that flat part, or the slant next to the mine(you may have landed on them anyways if you jumped far enough), which are right next to the slight slant that faces right, which is where you landed, and jump left. I like to land on the right side of the piece of the floor that kind of looks like a ^ sign and jump into the little crevice above that big vertical piece of wall. You can chill there or wall slide/jump/wall slide that wall below it for a bit if you need to catch your breath, just don't get squashed by a thwump coming back. *ALTERNATIVELY*, if you're shy about riding thwumps, the bottom part is doable just jumping through, it's just tricky. But if you're not riding on top of the thwumps, I would recommend riding on the side of the thwump that comes at you. You can do this by letting it come at you while you chill in the mine-less bottom right corner. Once it hits the wall, jump and wall slide its left side, and keep jumping and holding right, and you should be able to ride the sucker all the way to the little crevice. It takes awhile, but you should have plenty of time.
The decision is how to do this next part. Some people will jump off, land on the slant facing the wall on the ^ shaped part, jump to the wall, wall jump up, then wall jump the teeny vertical ledges. Personally, I always thought that was hard. So I like to chill in the little crevice, then hop up onto that baby corner right above it (yes, it's right next to the mines, so watch out). You don't need to stand on the ledge; you can just land the corner and jump immediately before you fall off. When you jump to the right off that corner, a lot of the time you'll have to wall jump off that tiny vertical ledge that's there top hop of to the flat ledge, where you can chill. Jump to the next ledge up, and don't worry about the switch (it's useless IMHO). Then jump up to the slanted part right above that ledge and chill.
This next part has a lot of variation, but I'll tell you what I find easiest. Highscorers jump further right and let the thwump go over them while they cut it close on a slant next to a mine, which is very hard, so I don't recommend. I recommend chilling on that slant you are on, above the ledges and hopping and holding right, so the thwump triggers and goes right over your head(with a significant amount of room). Then jump on the right side of the thwump (its back) and wall slide/jump/wall slide by jumping and holding left the entire time. You can hold on as long as you want, and depending on where you get off the thwump, your strategy changes a little. I like getting off of the thwump somewhere around the terminal switch, and I usually do it by jumping high on one of my wall slide jumps, landing on top of the thwump and jumping so it goes under me (or just clearing it with the first jump). You can do this pretty safely right before or right after the terminal switch (I prefer before, because you have more landing room). Then I wait in that flat area to the right of the terminal (you can wait on any surface you like, just don't get killed, and make sure themes a high ceiling) and when the thwump come back at me, I jump over it, let it go under (I usually land on the 45 degree right facing slant to the right of the terminal), then make the rest of my jumps. I jump from that 45 degree slant to the next small gap in the mines, a smaller slant that faces left, and then I hop (I think it's safer than a full jump) to the small flat gap between mines. Then I hop over to the slanted corner and wait (hop and wait, so I don't fall immediately).
This next part (next 2 corridors) is extremely difficult, and there's no way around it that I found. My favorite way to do it is very hard, but so is every other way. You have to trigger that thwump facing upwards by leaning over the edge or hopping. Then when it hits the top, fall off the ledge under it. There are three slants you can land on, and each has a way to survive.
This is where it gets extremely difficult. You can pick which ledge to land on, I'll explain each, and I'll put a number for each so you can know when I talk about each. I like to land on the ledge on the left (the steepest one), so I'll start by explaining that. (*1*) When you fall, land directly on the ledge, which will require a little steering, because if you fall straight down, you won't be far enough left to hit it. With the momentum of your fall, jump as soon as you hit the ledge, which is very hard, and then land in the small gap between mines (there's a flat part and a slanted part, but it's tough to land in that area because of the speed). Depending on how fast you were going and where you jump from, you will 9 times out of ten need to hold right to slow down your jump so you don't overshoot that small gap. Then jump immediately when you land to avoid the thwump coming from the left straight at you. You can jump straight up and come back down or you can jump up and left to the next piece of floor clear of mines, which is three mines away from where you landed. From there, just keep jumping from one small clearing to another 'til you are on that ledge at the end of the corridor(the jumps are hard, I know, but there's nothing I can do to help you with that). *Alternatively*, once you jump over the thwump that comes from the left side towards you, you can wait ‘til it comes back and ride the left side of it to the ledge like I have previously described. (*2*) Landing on the slant on the far right instead of the slant I talked about earlier is much the same. I don't like it because you have to watch out for the mines to even get to the slant to land on it, and once you land on it, the jump is harder. Anyways, once you land on the small slant on the right, do the exact jump as I described earlier, to the gap between a set of 3 mines and a set of 4 mines. Only now, the jump is farther. I have done this, so I know it is possible, but I think it's harder (personal opinion). (*3*) The middle ledge. You might think it's easier, because you don't have to jump right when you land on it, and for some it will be. Since you can't jump left with enough speed to beat the thwump coming towards you when you land in the middle, your only choice is to wait for the thwumps to come to you. On the other ledges, you didn't have to worry about when the timing with vertical thwump coming back down, but for this one it may make a big difference. The idea for this ledge is to wait for the vertical thwump to come back down, and jump up and left off your ledge into that little gap between the mine and the vertical thwump before it traps you. If you wait for the vertical thwump at the top of the descent, so that when you fall to this middle ledge, you barely beat the thwump coming back down (so you are pretty close to getting smashed between the corner you fall from and the thwump coming back down), if you do that, what happens is that the vertical thwump is closer to resetting when the thwump coming from the left triggers. This allows you enough time to trigger the vertical thwump again by jumping up and left (you may like to jump to the left-facing 45 degree slant to left of the middle slant to prevent being trapped) and so when that vertical thwump triggers for the second time, the left-right thwump goes underneath you. Then you can either ride that thwump over to the ledge on the left side of the corner, or wait in one of the safe parts and let it go under you, or you can go faster through this horizontal corridor than the thwump does coming back. The point is, if you can delay the thwump coming from the left triggering, it makes this easier, and the basic idea is get the vertical thwump out of the corner and make it so you don't have to deal with that thwump coming fast at you from the left. It's a tricky jump triggering the vertical thwump from that lower right corner so that the left-right thwump doesn't kill you, but you may find it easier than executing the jumps from the other ledges.
Any way you do that last part, it's probably going to be very hard, and you end up on the small ledge on the left part of the corridor. This vertical corridor is small and nothing happens in it, so I recommend gathering your thoughts and focusing for the last part, which is hard. Just jump your way to that top small slant that faces right, and get ready.
The last part is the most intense. You start from that little slant at the start of the corridor (the thwump won't trigger yet, so don't worry). The next jumps are precision jumps that require skill and speed. From that slant, jump to the SECOND gap in the mines (there’s a piece of gold over each gap). The second one is MUCH easier to hit for me, and it makes clearing the thwump easy. The thwump triggers as you land, so from that second gap, jump high and to the right a little, and follow the ceiling to land in the last gap in the mines. Then jump high and to the right again, and follow the ceiling again right to the door. Congrats, you made it!